I wouldn't worry about finding this "B". The definition of "row space of A" is the space spanned by the rows of A. In order to prove that < 3 1 2 3> is in that rwo space, you must show that it can be written as a linear combination of rows of A: that is, find a, b, c such that a<2 4 1 1>+ b<3 4 0 2>+ c<1 2 1 2>= <3 1 2 3>. That is the same as showing that it is possible to solve 2a+ 3b+ c= 3, 4a+ 4b+ 2c= 1, a+ c= 2, and a+ 2b+ 2c= 3.